This blog is about how undergraduate mathematics is taught at the University of Michigan. This means that it will have many different things going on: there is a lot of undergraduate mathematics taught here, in many ways and to many people.

In any given academic year the Mathematics Department has over 11,000 undergraduate student course enrollments in roughly 400 course sections. In just our “big three” Introductory Program courses (precalculus, math 105; calculus I, math 115; and calculus II, math 116) we see over 4,200 course enrollments each year. The students we teach are drawn from many different populations, including science and engineering students coming to learn the language that underlies much of what they do; students aiming for financial careers, including those applying to the business school; prospective medical and law school applicants; future teachers; students fulfilling distribution requirements for their college; and, of course, mathematics majors and other students who just truly enjoy mathematics.

Naturally, there are many things that differ between the sections and courses these students take. For example, some courses (in particular, the Introductory Program courses) have common homework and exams across all sections, and some courses, well, don’t. Some courses are taught in a large lecture format and others are taught in a small interactive setting. But there are also many common threads that run among our courses. We have high expectations for our students. All new instructors undergo intensive training. And inquiry-based learning approaches are employed in the Introductory Program, in courses taught in connection with our Inquiry Based Learning center, and in many other courses. This blog is a place for these differences and commonalities to be explored, and for discussion of what works and how.

There is, of course, the standard *caveat emptor* associated with the posts here: not everything that is done in our classrooms works, and what is written here will be a sampling of many things. Some of them may be cautionary tales. Some of them may be things that worked well. Some of them may simply provoke some thought and discussion. We hope so, in any case.